Topological Insulators
R. Ramesh
Annual Retreat
August 21, 2012
A Science & Technology Center
Topological Insulators
R. Ramesh
Annual Retreat
August 21, 2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Correlated Oxides
Band Insulator
Mott Insulator LaTiO3 : d
1 state, BUT insulating
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Topological Insulators Three broad classes of insulators
Band, Correlated and Topological
Insulator
Metallic Surface
• Bulk is an insulator, but the surface is conducting! • Driven by strong Spin-Orbit interaction. • It is a topological order, i .e. all the “good” properties are robust
against small perturbation.
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Topological Insulators Three broad classes of insulators
Band, Correlated and Topological
8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Topological surface state
Qi and Zhang, Rev. Mod. Phys. 83, 1057–1110 (2011)
• At surface states, electron spin and momentum are locked. • Potential platform for spintronics applications. • Spin chirality also prevents electrons from back scattering.
8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Large MR in GeTe-Sb2Te3 Multilayers
Tominaga et al, APL 2012 8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Research Directions
Pyrochlore Iridates Perfect epitaxial quality
Interfaces with band insulators Probe interface transport
XAS studies
Perovskite Iridates Strain control of transport
Doping effects : e- h-
Interfaces : electric field control
8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
1 meV 10 eV 1 eV 100 meV 10 meV 100 μeV
H=HKin+Ve-ion+Ue-e+HHund+Hs-s+He-ph+Hs-o
kinetic interaction
e-ion interaction
e-e interaction
Hund’s interaction spin-spin interaction
e-phonon interaction
crystal field
spin-orbital interaction
DM interaction
1 V/nm 0.1 V/nm 10 V/μm 1 V/μm Electric Field
100 T 10 T 1 T Magnetic Field
1000 K 100 K 10 K 1 K
Temperature
10 % 1 % 0.1 % 0.01 %
Epitaxial Strain
Interactions in complex oxide materials
Pyrochlore Iridates – Ln2Ir2O7
• Iridium 5d electrons has a strong spin-orbit coupling (0.2-1eV), comparable to correlation energy scale (1-2eV).
• Geometric frustration in the pyrochlore lattice leads to non-trivial topological effect.
• Pyrochlore iridates is the model system for oxides topological insulator
8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
TBI : Topological Band Insulator TMI : Topological Mott Insulator GMI : Gapless Mott Insulator
Rich phase diagram of iridates
By tuning different energy scales, several exotic topological order emerge
Pesin and Balents, Nature Physics 6, 376 (2010) Wan, Vishwanath et. al. Phys. Rev. B 83, 205101 (2011) 8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Pyrochlore iridates thin films
Substrate: YSZ
Y2Ti2O7 , Bi2Ti2O7, etc
Eu2Ir2O7
27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.02Theta-Omega (°)
0.1
3
1
3
10
3
100
3
1000
3
10000
3
100000
Inte
nsity (
counts
)
Our approach: thin film hetrostuctures grown by laser MBE, offering precise control of materials and interface. Create TI/ BI interfaces using epitaxy Explore transport at interfaces
Burkov and Balents, PRL 2011
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Other examples of Strong Spin-Orbit Coupling :
Conducting domain walls in BiFeO3 Strong interface magnetism in LSMO/BFO
Strain effects on Sr2IrO4
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Rhombohedral, R3c
apc = 3.96Å MFe2
[111]
MFe1
M
G-type AFM order
• TC ~ 830°C; Polarization along [111]
• G-type, TN ~ 370°C
• Strong correlations ; Bandgap ~ 2.6eV
• Small canted moment in bulk 8emu/cc
Magnetoelectric Multiferroic BiFeO3
71
°
180
°
109
°
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Domain Walls : Natural Atomically Sharp Interfaces
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Domain Walls : Natural Atomically Sharp Interfaces
FE Wall Width : 1-3nm 8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Domain Walls : Natural Atomically Sharp Interfaces Magnetotransport through109° Domain Walls
0 50 100 150 200 250 300
0
50
100
150
200
250
300
350
R(
10
9
)
Temperature (K)
0 T
8 T
-50
-40
-30
-20
-10
0
R
/R0 (%
)
MR
-10 -5 0 5 10-100
-50
0
50
100
Cu
rre
nt
(pA
)
Voltage (V)
0 1 2 3 4 5 6 7-80
-60
-40
-20
0
20
R
/R0 (
%)
Magnetic Field (T)
H DW, in-plane
H out-of-plane
HDW, in-plane
Fitting
5
10
15
20
25
R (
10
9 )
3K
Metallicity at walls Spin Transport
How to enhance ?
He et al, PRL, Feb 2012 8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
MnO2-BiO-FeO2 Interface
(BiO Interface)
MnO2-La0.7Sr0.3O-FeO2 Interface
(La0.7Sr0.3O interface)
Atomic Scale Design of Charge, Spin and Orbital Degrees of Freedom at Heterointerfaces
Yu et al, PRL, 2010 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Atomic Scale Design of Charge, Spin and Orbital Degrees of Freedom at Heterointerfaces
La0.7Sr0.3O Interface
SRO
2 μm
AFM:SrTiO3
Yu et al, PRL, 2010
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
60 80 100 120 140
55 Mn
88 Sr
139 La
MnO 2 term
La 0.7
Sr 0.3
O term = 5 o
MS
RI In
ten
sit
y (
a.u
.)
Atomic number
Time of Flight Surface Spectroscopy to probe average surface termination
Yu et al, PRL, 2010
8/21/2012
705 710 715 720 725 730 735-6
-4
-2
0
2
4
6
8
XM
CD
(%
)
Photon Energy (eV)
Interface BiFeO3
GaFeO3
-Fe2O
3
Bulk BiFeO3
Atomic Scale Design of Charge, Spin and Orbital Degrees of Freedom at Heterointerfaces
Yu et al, PRL, 2010
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Yu et al, PRL, 2010
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
-1200 -800 -400 0 400 800 1200
-3
-2
-1
0
1
2
3
Mag
neti
zati
on
(/M
n)
Magnetic Field (Oe)
5 nm LSMO + 30 nm BFO
0.2 T FC
-0.2 T FC
5 nm LSMO
1 T FC
(a)
Yu et al, PRL, 2010
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Dynes, et al Nature Materials 2010
Controlling Exchange Coupling with E-Field
+60V
-60V
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Dynes, et al Nature Materials 2010
660 690 720 750 780 810
Co L2
Co L3
Fe L2In
tens
ity
(a. u
.)
Energy Loss (eV)
Fe L3
EELS analysis at the interface BFO/CoFe
BFO
SRO / DSO
Co.90Fe.10
BFO
Pt
V
BFO
SRO
DSO
Sharp interface at the
atomic scale
Essential at the
magnetoelectic
interface
BFO- Ferromagnetic Metal Interfaces
8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Magnetization reversal @RT, non
volatile and reversible
PFM IP
PFM IP
Out of plane, reversible switching of M
8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
Sr2IrO4 J. Phys.: Condens. Matter 20 (2008) 295201 Y Klein and I Terasaki
z = 3/4 z = 1/4
z = 0 z = 1/2
11oO
Sr
Ir
Figure 1. Structure of Sr2IrO4. Sr, Ir and O elements correspond tolarge green spheres, medium grey spheres and small red spheres,
respectively.
the gap at EF has not yet been clarified, but it is found to be
responsible for the insulating transport properties of Sr2IrO4,
which may discriminate 5d TMOs, from two 4d TMOs such
as Sr2RhO4 and Sr2RuO4. We expect that the difference in
experimental and theoretical results is due to some many-body
effect because that kind of phenomenon is not fully considered
in band calculations. Although an electronic specific heat was
measured to be γ ≈ 2 mJ K− 2 mol(Ir)− 1 [10], it does not
always mean weak correlation, because the carrier density is
reduced by the opening of the gap.
It was reported that Ca2+ and Ba2+ can be substituted
for Sr2+ by a small fraction, which does not change the
magnetic and transport properties [12]. This may be due to
the similar electronic configuration of these three alkaline-
earth elements. In the present work, two kinds of cationic
substitutions have been tried in order to tune the properties of
Sr2IrO4 and get some insight on its electronic state. Sr has been
substituted with La in order to see the response of the material
to electron doping. Rh has been inserted on the Ir lattice as a
perturbative element of the magnetic environment. Resistivity
(ρ), thermoelectric power (S) and magnetization (M) have
been measured and analysed. The electrical resistivity itself
is insufficient to understand the transport properties because
it depends on extrinsic phenomena such as grain-boundary
scattering and cannot distinguish n-type from p-type carriers.
We need another probe that is less affected by grain boundaries.
The thermoelectric power and the Hall coefficient are relevant
in the case of polycrystalline samples [13]. Here we show
results of thermoelectric power measured below 300 K.
2. Experimental details
Sr2− xLax IrO4 (x = 0 and 0.05) and Sr2Ir1− yRhyO4 (y = 0.05,
0.1 and 0.2) polycrystalline samples were synthesized from the
solid state reaction of SrCO3, IrO2, La2O3 and Rh2O3 powders.
Mixtures were heated in air at 900 ◦ C for 24 h, 1000 ◦ C for
Figure 2. X-ray diffraction patterns of the polycrystalline samplesSr2− xLax IrO4 (x = 0 and 0.05) and Sr2Ir1− yRhyO4 (y = 0.05, 0.1and 0.2). The Cu Kα is used as an x-ray source.
24 h and 1100 ◦ C for 60 h with intermediate grindings. Note
that this conventional technique is completely different than
the rapid heating and quenching technique used recently to
synthesize Sr2− xLax IrO4 [14].
The x-ray diffraction was measured using a standard
diffractometer with Cu Kα radiation as an x-ray source in
the θ–2θ scan mode. The resistivity was measured though
a four-terminal method, and the thermoelectric power was
measured using a steady-state technique with a typical gradient
of 0.5 K cm− 1. The magnetic properties were studied with
a dc SQUID magnetometer (2–400 K, 0–7 T) by recording
magnetization as a function of temperature.
2.1. Structural analysis
Figure 2 shows the x-ray diffraction patterns of the sintered
samples. All the peaks are indexed according to the I41/ acd
space group. This shows that La and Rh are substituted for
Sr and Ir, respectively. For La content exceeding x = 0.05,
we observed a tiny peak corresponding to some unknown
impurity. As a consequence, the solubility limit of La to
Sr is determined to be x = 0.05. In figure 3, we plot the
evolution of the cell parameters as a function of the La and
Rh contents. For the mother compound, the a and c axes
have been reported many times with different values, ranging
from 5.4921 to 5.4994 Å for a and 25.766 to 25.798 Å for
c [6, 9, 11, 12, 14, 15]. We calculated the lattice constants to
be 5.4955 Å and 25.783 Å for a and c, respectively, which are
in the range of the reported values. Concerning the effect of
2
Klein & Terasaki, J. Phys.: Cond. Mater. (2008) 8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.
0 90 180 270 360 (deg)
Inte
nsity (
arb
. units)
(b) (a)
(c) SrTiO3(101)
Sr2IrO4(116)
10 20 30 40 50 6010
0
105
2 (deg)
Inte
nsity (
arb
. u
nits)
STO(002) STO(004) SIO(00 12)
SIO(00 8)
SIO(00 4)
SIO(00 16)
4.63 nm
0.04 nm
1.0µm
Ir
Sr
[100]SrTiO3
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
40 42 44 46 48
1010
1015
1020
2 (deg)
Inte
nsity (
arb
. units)
Qx (Å
-1)
Qy (
Å-1
)
0.93
0.935
0.94
Qx (Å
-1)
Qy (
Å-1
)
0.93
0.935
0.94
Qx (Å
-1)
Qy (
Å-1
)
-0.366 -0.365 -0.364 -0.363 -0.362
0.93
0.935
0.94
Fig. 2 Selectable unit cell distortion via thin film thickness
(b) 5 nm
10 nm
60 nm
(a) SrTiO3( 0 0 2)
(c)
(d)
5 nm
10 nm
60 nm
8/21/2012 For Internal E3S Use Only
These Slides May Contain Pre-publication Data and/or Confidential Information.
Fig. 3 Strain induced transition from 2-D towards 3-D system
Room temperature X-ray linear dichroism decreases with increasing strain. Data shows a strain-induced transition from a layered 2-D system (60 nm) {strong difference between horizontal and vertical absorption} into a 3-D scenario {less difference between horizontal and vertical absorption}. This is in excellent agreement with the collapse of c-parameter observed in X-ray diffraction and anticipates a transport mechanism scenario more similar to Sr3Ir2O7 or SrIrO3 compounds.
8/21/2012 For Internal E3S Use Only
These Slides May Contain Prepublication Data and/or Confidential Information.
Fig. 4 Strain-tuned electrical transport mechanism. 100% reduction of activation energy at 300 K
ε[100] = 0.17%
ε[100] = 0.23%
ε[100] = 0.31%
8/21/2012 For Internal E3S Use Only
These Slides May Contain Prepublication Data and/or Confidential Information.
SIO
BFO
STO
BFO/SIO/STO
8/21/2012 For Internal E3S Use Only These Slides May Contain Prpublication Data and/or Confidential Information.
Going Forward
Pyrochlore Iridates Perfect epitaxial quality
Interfaces with band insulators Probe interface transport
XAS studies
Perovskite Iridates Strain control of transport
Doping effects : e- h-
Interfaces : electric field control
8/21/2012
For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.